A new preprint reports a difference between two ways of setting up tetraquark calculations. The version with a fuller spatial basis contained resonance poles that the H-only version did not resolve: two additional poles in a strange-charm system and four new compact poles in a double-charm system. The comparison therefore concerns the number of resonance candidates as well as their locations.
The coordinate test
Jacobi coordinates are different relative-position variables used to build the spatial basis. The researchers compared conventional H-type configurations with a basis that combined H-type and all K-type configurations. They optimized Gaussian basis parameters stochastically and used complex scaling to identify bound and resonant states. The modeled systems covered open-flavor, doubly heavy, fully heavy and fully strange tetraquarks. In the paper's notation, Q was charm or bottom and n was up or down. There was no participant sample; the analysis units were modeled systems and extracted poles.
Strange and charm systems
In the strange-charm system, the scalar channel yielded a bound state at 2350 MeV, 3.8 MeV below the theoretical D K-bar threshold. The reported bound-state radii suggested a molecular spatial structure. The same calculation also produced a resonance pole at 2903 - 10i MeV. The paper reports such resonances as complex energies, with i denoting the imaginary unit.
The all-Jacobi comparison in that strange-charm channel reported two additional poles at 2994 - 3i MeV and 3122 - 4i MeV. They were unresolved in the H-only calculation. The contrast is important because the restricted and expanded calculations do not return the same list of candidates.
Bound states in heavier combinations
The strange-bottom case gave masses of 5779 and 5838 MeV, with binding energies of -5.3 and -3.0 MeV, respectively. Binding energy here is the reported energy difference relative to the stated threshold. The calculation gives these as model predictions, with mass precision described as being on the order of tens of MeV.
For the isoscalar bottom-bottom system, the calculation produced bound states at 10491 and 10642 MeV, with binding energies of 153 and 2 MeV. The first result is much more deeply bound than the second within the calculation.
In the all-Jacobi double-charm calculation, a bound state appeared at 3863 MeV with binding energy -15 MeV. A comparison of internal root-mean-square distances indicated a D*D molecular configuration for this near-threshold state. The paper treats that structural classification as qualitative and notes model uncertainty on the order of tens of MeV.
More poles in the double-charm spectrum
The same double-charm calculation produced four new compact poles at 4380 - 3i, 4511 - 6i, 4529 - 0.1i and 4555 - 1i MeV. Two H-only poles, at 4542 - 10i and 4631 - 3i MeV, lacked robust counterparts in the all-Jacobi result. The root-mean-square radii of a nearby pole were numerically unstable as the complex-scaling angle changed, so the associated compact description should be read cautiously.
A mixed picture in fully heavy systems
The fully charmed calculation was presented as a set of compact resonance candidates associated with X(6900) and X(7200). Reported poles included 6979 - 36i, 7013 - 38i, 6995 - 34i and 7126 - 6i MeV. They remain theoretical candidates, not confirmed experimental identifications.
In the 2++ fully charmed comparison, the all-Jacobi values for two poles were 7013 - 38i and 7126 - 6i MeV, compared with 7012 - 39i and 7128 - 6i MeV in the H-only calculation. An additional state appeared at 7045 MeV. Taken with the new strange-charm and double-charm poles, this gives a mixed picture: some poles shift slightly, while other candidates appear only in the fuller basis.
The calculation's limits
Fully strange systems produced a different pattern. No compact S-wave resonances were reported below 2.6 GeV, while a 2++ resonance near 2.7 GeV was proposed.
The model's widths also need careful reading. It omitted finite constituent-meson widths and considered only two-body strong decays; the authors say the calculated widths are expected to underestimate actual widths. The paper describes some states as pseudo-bound because the corresponding decay thresholds are absent, and treats them as intrinsically physical P-wave scattering states.
The supplied document is an arXiv version-1 preprint dated 28 August 2026. The reported mass precision is on the order of tens of MeV, so the numerical values should be read as estimates from the stated model calculation.
Paper data and sources
Original title: Investigation of S-wave tetraquark bound and resonant states with all Jacobi coordinates
Authors: Xin-He Zheng, Yao Ma, Liang-Zhen Wen, Shi-Lin Zhu
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text